How to read piano sheet music for beginners

Mathematics and Music

Hsiu-Hui Peng Chen

There are numerous researches probing the relationship between the mathematics and music. The interplay between the two subjects has also been a common topic in many science fair projects and student essays as well. A popular conjecture is that the frequent, rhythmic touches between finger tips and the piano keyboard produce a sequence of mild, pulsating impulses that transmit through the nerve system to stimulate the intellectual growth and development of human brains. As a piano teacher, I have always been intrigued by the magical connection bridging these two very different realms of disciplines. Since I am not a music or mathematics researcher, I do not have a systematic data to support the claims. What I can offer in this article is based on my personal observation on the developments of many piano students in my twenty-five years of piano teaching experience. It is interesting and fascinating.

Music and math have always been an integral part of my daily life, as a child, a college student, and even now as a mother of two. I began giving private piano lessons while I was still a college student, and I have continued to learn from teaching numerous piano students. This experience offers me a unique opportunity to observe up close my piano students’ developments in music as well as in academics. The ages of my students range from the slight age of 3 to the ripe age of 50. The bulk of my students are in grade school. Many of them struggle with surges of teen-age hormones, unstable emotions, parents and peer pressures. The process of mastering a complicated piano piece can be stressful, but playing a well-versed piano music tranquilizes the fretting mood and helps maintain a peaceful state of mind. The topic of my interest focuses on the effects of piano learning on young children’s (ages 3-12) mathematics development. The discussions will be focused on the three areas as follows:

• How does a solid math education support a student’s music development?
• How does music in a student’s life support his mathematic achievement?
• What is the connection between math and music?

How does a solid math education support a student’s music development?

There have been a lot of researches and many theories attempting to prove that learning an instrument in early childhood helps stimulate a person’s intellectual growth and development. Doctors and nurses around the world are beginning to suggest the parents of newborns to play classical music for the baby during the feeding and before bed, in belief that it will stimulate certain portions of the human brain. As a music teacher, I pay particular attention to when children can move to the next level of actively playing music as opposed to passively listening to it.

When is a child ready for music lessons? For example, in my own experience, a three-year-old child lacks the attention span of an older child of, say, 10 years of age. The young child is able to focus for a maximum of half an hour with his teacher before getting distracted. For children this young, I begin by teaching them the concept of their five fingers: the number 1, 2, 3, 4, and 5.We have five fingers on each hand, and we use them everyday for daily tasks such as picking up food, making a fist, opening doors, etc. We depend on our hands for a lot of menial tasks. Music requires a higher level of attention to the fiver fingers, and piano is especially demanding. Piano players need to use both hands and the player must follow the fingerings depicted on the music sheet. Pianists need to have a precise control of their fingers, for piano requires the use of both hands, all ten fingers at all times. Once the student advances to the point of playing music that requires both hands, it is very important that, no matter how young the child is, I enforce the numbers 1, 2, 3, 4 and 5 to correspond to thumb, index, middle, ring, and pinky fingers respectively, Figure A [1]. I require them to memorize the relation between the fingers and their respective numbers until it nearly becomes a second nature to them. It is only after I see that the student has firmly grasped this fundamental idea that I begin to teach them to read the notes on music sheets.

It’s hard to over-emphasize the importance of the fiver finger pattern, especially for those young beginners. Figure B depicts how to use the simple method of finger numbering to play the melody formulated in a formal music sheet shown in Figure C [1]. I often use such diagrams to help young students understand and reinforce the concept that relates numbers to their fingers.

Figure A

Figure B

Figure C

In addition to emphasizing the numerical order of fingers, as a piano teacher, I also have to explain many related math concepts to my students regardless of their ages. In order to prepare them to meet the music challenges ahead, I have to build a math foundation for them as a sustaining system, even if they are too young to make a proper sense out of math. The time signature of the music is always depicted on the very left side of each staff. For example,

3  3 beats total in a measure

4  the quarter note will have a value of one beat

6  6 beats total in a measure

8  the 8^th note will have the value of one beat

i.e, 2 eighths = 1 quarter

So, in Group A, counts as 1 beat, and one and a half beats, two beats, and three beats.

But, in Group B, counts as 1 beat, two beats, three beats, and four beats.

Compared Group B with Group A, we can see that each note in Group B receives double beats. This concept is actually a multiplication in disguise. As demonstrated in many children's learning results, students are better oriented to mathematical concepts if they are frequently exposed to practical examples, which have been methodically incorporated into their daily learning. Five finger pattern and various beat counting methods are two of such examples in piano music. Quite often we see that children who take piano lessons prior to grade school often have an advantage over their peers who have never previously been exposed to such mathematical concepts. And once they reach the 1^st or 2^nd grade, they will have a much easier time picking up elementary arithmetic skills.

Basic mathematic concepts, such as addition and multiplication, are instrumental for music learning. This is not only true for the young beginners but for intermediate and advanced pianists as well. In fact, it is even more important for the more advanced students to have a sounder mathematic background to achieve an accurate, flawless performance. Most students have little trouble playing notes with even numbered ratios, for example, in what I like to call “2 match 1” (quarter notes on one hand, 8^th on the other hand), or “4 match 2” (16^th notes on one hand, 8^th notes on the other). However, some pieces call for triplets on the one hand, and 8^th notes on the other hand. I call this “3 against 2”, and these types of music pieces demand infinitely more concentration to be played accurately. As the performance level gets higher, students inevitably encounter music literature that requires more challenging two-hand coordination such as "5 against 3," so on and so forth. Examples of more complicated combinations are given below:

1. Arabesque in E Major (by Debussy) [2]

Figure D

This piece of music, Figure D, begins with a single hand triplet. At measure 6 the right hand (upper clef) contains triplets and the left hand builds up by 8^th notes, giving the student some three-against-two action.

2. Clair de Lune (by Debussy) [2]

Figure E

This piece, Figure E, has a time signature of 9/8 (the 8^th note gets one beat and there are 9 beats total in a measure). This key signature makes it difficult to count the beats as 9 beats per bar, so, instead, we count it in sets of 3 per measure to make it more logical for the musician. This approach enables a student to interpret the music as a piece of music with ¾ times signature but at a slower tempo.

3. Fandaisie- Impromptu (by Chopin) Op. 66 [3]

Figure F

6

This music, Figure F, shows the time signature of ￠ which means that we use as one count; that is, note values are all cut in half. The left hand part is built up by

Thus, the left hand part which is composed of six 8^th notes is now counted as 1 half note. The right hand part is built up by eight 16^th notes, which are also counted as 1 half note. Essentially, for every note played by the left hand, the right hand has to match it by playing 8 evenly-spaced 16^th notes. And this is no simple task. I find it helpful if the students start off by playing the rhythm as if it were 4/4 and try to match four 16^th notes on the right hand to three 8^th notes on the left hand (4-against-3). Once the students can do this evenly, the tempo is then gradually increased until the rhythm can be accurately played in the 2/2 time signature. Simplifying the key signature is a very powerful way to help the student master the technique and structure of a difficult music piece composed with a complex time signature.

4. Nocturnes Op. 9 No. 1 (by Chopin) [4]

Figure G

Let's examine the 2^nd measure in Figure G first. The right hand contains eleven 8^th notes which are played throughout the duration of three beats, while the left hand contains six 8^th notes which are also played throughout a total of three beats. Now, let's try some simple math: if we divide 11 by 6, the result is 1.83333. Students will never go far if they really try to count the beat by following the irrational number. The knack is that students should be able to use their well-established yet simple math concepts, aided by sufficient practices to build up the required muscle memory, which in turn trains our brain to develop a high degree of balance for both hands to meet such a challenge.

The above four illustrations are examples, on the technical side, to explain how math helps students better dissect, understand, and interpret complex music pieces. This is especially important for pianists who solely rely on counting the beats to achieve a perfect coordination of both hands. On my collective observation over groups of students, I also notice an interesting phenomenon to share with interested readers.

The middle and high schools in Ann Arbor School District annually participate in a well-organized “Solo & Ensemble” event, in which band and orchestra students are given an opportunity to perform to professional musicians and receive a rating of their achievements in a scale of 1 to 5 (1 being excellent, 5 being below par). Students who receive the 1^st division rating are qualified to proceed to the State Semi-finals, a rare honor that motivates aspiring students across Michigan to participate. I’ve noticed that many students who are qualified to enter the State level competition and earn recognitions are those who have also demonstrated rather satisfactory math ability in school.

How does music support math?

The process of practicing and learning a piece of music itse